WHY CITIES KEEP GROWING, CORPORATIONS AND PEOPLE ALWAYS DIE, AND LIFE GETS FASTER

The question is, as a scientist, can we take these ideas and do what we did in biology, at least based on networks and other ideas, and put this into a quantitative, mathematizable, predictive theory, so that we can understand the birth and death of companies, how that stimulates the economy?

For the past few years Geoffrey West, a physicist former president of SantaFe Institute has been calling for "a science of how city growth affects society and environment".

After years of focusing on scalability of cities and urban environments, West, is now is bringing "some of the powerful techniques, ideas, and paradigms developed in physics over into the biological and social sciences". He is looking at a bigger picture and asking the following question: "to what extent can biology and social organization (which are both quintessential complex adaptive systems) be put in a more quantitative, analytic, mathemitizable, predictive framework so that we can understand them in the way that we understand 'simple physical systems'?'

West interprets. He speculates. …

The great thing about cities, the thing that is amazing about cities is as they grow, so to speak, their dimensionality increases. That is, the space of opportunity, the space of functions, the space of jobs just continually increases. And the data shows that. If you look at job categories, it continually increases. I'll use the word "dimensionality." It opens up. And in fact, one of the great things about cities is that it supports crazy people. You walk down Fifth Avenue, you see crazy people. There are always crazy people. Well, that's good. Cities are tolerant of extraordinary diversity. ...

This is in complete contrast to companies. The Google boys in the back garage so to speak with ideas of the search engine, were no doubt promoting all kinds of crazy ideas and maybe having even crazy people around them.

Well, Google is a bit of an exception, because it still tolerates some of that. But most companies start out probably with some of that buzz. But the data indicates that at about 50 employees to a hundred that buzz starts to stop. A company that was more multi dimensional, more evolved, becomes uni dimensional. It closes down.

Indeed, if you go to General Motors or you go to American Airlines or you go to Goldman Sachs, you don't see crazy people. Crazy people are fired. Well, to speak of crazy people, is taking the extreme. But maverick people are often fired.

It's not surprising to learn that when manufacturing companies are on a down turn, they decrease research and development, and in fact in some cases, do actually get rid of it, thinking this is "oh, we can get that back in two years we'll be back on track."

Well, this kind of thinking kills them. This is part of the killing, and this is part of the change from superlinear to sublinear, namely companies allow themselves to be dominated by bureaucracy and administration over creativity and innovation, and unfortunately, it's necessary. You cannot run a company without administrative. Someone has got to take care of the taxes and the bills and the cleaning the floors and the maintenance of the building and all the rest of that stuff. You need it. And the question is, “can you do it without it dominating the company?” The data suggests that you can't.

The question is, as a scientist, can we take these ideas and do what we did in biology, at least based on networks and other ideas, and put this into a quantitative, mathematizable, predictive theory, so that we can understand the birth and death of companies, how that stimulates the economy? How it's related to cities? How does it affect global sustainability and have a predictive framework for an idealized system, so that we can understand how to deal with it and avoid it? If you're running a bigger company, you can recognize what the metrics are that are driving you to mortality, and possibly put it off, and hopefully even avoid it.

Otherwise we have a theory that tells you when Google and Microsoft will eventually die, and die might mean a merger with someone else.

Read on.

— JB

WHY CITIES KEEP GROWING, CORPORATIONS AND PEOPLE ALWAYS DIE, AND LIFE GETS FASTER

[Geoffrey West:] I spent most of my career doing high-energy physics, Quarks, dark matter, string theory and so on. Between ten and fifteen years ago I started to get interested in the question of whether you can take some of the powerful techniques, ideas, and paradigms developed in physics over into the biological and social sciences. And of course, some of that has obviously been done with spectacular success. But the question was, in a bigger picture, to what extent can biology and social organization (which are both quintessential complex adaptive systems) be put in a more quantitative, analytic, mathematizable, predictive framework so that we can understand them in the way that we understand "simple physical systems"?

It is very clear from the beginning that we will never have a theory of biological and social systems that is like physics — that is, something that's precise that we can predict, like for example, the motion of the planets with great precision or the magnetic electron to 12 decimal places. Nothing approaching that can possibly be in these other sciences, because they are complex systems.

Nevertheless, that doesn't mean that you couldn't have a quantitative theory. It would simply mean that you would possibly have a theory that is cross-grained. Meaning that you would be able to ask questions, big questions, and answer them in an average idealized setting.

For example, we might ask questions about aging and mortality. Why is it that human beings live over the order of a hundred years? What about a thousand years, ten years, or a million years? Where does that number come from? What is the mechanism of aging? Can we quantify it in some way and understand where that hundred years comes from for a human being, and why it's only two to three years for a mouse, when it's the same stuff, so to speak? And how is that related to microscopic time scales in genes and respiratory complexes? So how did microscopic numbers somehow exponentiate into macroscopic numbers? And that brings up all kinds of questions about aging itself, life span, and so on. So that's the paradigm.

I started working some years ago on questions in biology. I started using the very powerful techniques developed in physics, and that have run through the history of physics, to think about scaling phenomena. The great thing about scaling is that if you observe scaling (that is, how the various characteristics of a system change when you change its size) and if you see regularity over several orders of magnitude, that typically means that there are underlying generic principles, that it is not an accident. If you see that in a system, it is opening a window onto some underlying, let's use the word, "universal principle".

The remarkable thing in biology that got me excited and has led to all of my present work (which has now gone beyond biology and into social organizations, cities, and companies) is that there was data, quite old and fundamental to all biological processes, about metabolism: Here is maybe the most complex physical chemical process possibly in the universe, and when you ask how it is scaled with size across mammals (as an example to keep it simple) you find that there is an extraordinary regularity.

This is surprising because we believe in natural selection, and natural selection has built into it this idea that history plays an important role. There's the environmental niche for every organism, every component of an organism, every cell type is unique and has its own unique history. So if you plotted, for example the metabolic rate on the Y axis and size on the X axis, because of the extraordinary diversity and complexity of the system and the historical contingency, you would expect points all over the map representing, of course, history and geography and so on.

Well, you find quite the contrary. You find a very simple curve, and that curve has a very simple mathematical formula. It comes out to be a very simple power law. In fact, the power law not only is simple in itself mathematically, but here it has an exponent that is extraordinarily simple. The exponent was very close to the number three quarters.

First of all, that was amazing in itself, that you see scaling. But more importantly was that the scaling is manifested across all of life into eco-systems and down within cells. So this scaling law is truly remarkable. It goes from intracellular up to ecosystems almost 30 orders of magnitude. They're the same phenomenon.

Furthermore, if you look at any physiological variable, such as the rate at which oxygen diffuses across lungs, the length of the aorta, anything to do with the physiology of any organism, or if you look at any life history event like how long you live, how long does the organism live, how long does it take to mature, what is its growth rate, etc., and you ask how does it scale? It scales in very similar way.

That is, it scales as a simple power law. The extraordinary thing about it is that the power law has an exponent, which is always a simple multiple of one quarter. What you determine just from the data is that there's this extraordinary simple number, four, which seems to dominate all biology and across all taxonomic groups from the microscopic to the macroscopic.

This can hardly be an accident. If you see scaling, it is manifesting something that transcends history, geography, and therefore the evolved engineered structure of the organism because it applies to me, all mammals, and the trees sitting out there, even though we're completely different designs.

The big question is where in the hell does that number come from? And what is it telling us about the structure of the biology? And what is it telling us about the constraints under which evolution occurred? That was the beginning of all this.

I'll say a few words about what we propose as the solution. But to jump ahead, the idea was that once we had that body of work, understanding the origin of these scaling laws was to take it over into social organizations. And so the question that drove the extension of this work was, “are cities and companies just extensions of biology?”

They came out of biology. That's where they came from. But is New York just actually, in some ways, a great big whale? And is Microsoft a great big elephant? Metaphorically we use biological terms, for example the DNA of the company or the ecology of the marketplace. But are those just metaphors or is there some serious substance that we can quantify with those?

There are two things that are very important that come out of the biology of the scaling —it’s theoretical and conceptual framework.

One: Since the metabolic rate scales non-linearly with size — all of these things scale non-linearly with size — and they scale with exponents that are less than one, what that means is that if the metabolic rate per cell is decreasing with size, the metabolic rate of our cells, my cells, are working harder than my horses. But my dogs are working even harder, in a systematic predictive way.

What does that say? That says there's an extraordinary economy of scale.

Just to give you an example, if you increase the size of an organism by a factor of ten to the fourth, four is the magnitude, you would have expected naively to have ten to the fourth times as much energy. You would have the ten to the fourth times more cells. Ten thousand times more cells. Not true. You only need a thousand times. There's an extraordinary savings in the energy use, and that cuts across all resources as well.

When we come to social organizations, there's an interesting question. Do we have economies of scale or what? How do cities work, for example? How do companies work in this framework? That's one thing.

The second thing is, (again, comes from the data and the conceptual framework explains it) the bigger you are, the slower everything is. The bigger you are, you live longer. Oxygen diffuses slower across your various membranes. You take longer to mature, you grow slower, but all in a systematic, mathematizable, predictable way. The pace of life systematically slows down following these quarter power scales. And again, we'll ask those questions about life ... social life and economies.

The work I got involved in was to try to understand these scaling laws. And to make it a very short story, what was proposed apart from the thinking was, look, this is universal. It cuts across the design of organisms. Whether you are insects, fish, mammals or birds, you get the same scaling laws. It is independent of design. Therefore, it must be something that is about the structure of the way things are distributed.

You recognize what the problem is. You have ten14cells. You have this problem. You've got to sustain them, roughly speaking, democratically and efficiently. And however natural selection solved it, it solved it by evolving hierarchical networks.

There is a very simple way of doing it. You take something macroscopic, you go through a hierarchy and you deliver them to very microscopic sites, like for example, your capillaries to your cells and so on. And so the idea was, this is true at all scales. It is true of an ecosystem; it is true within the cell. And what these scaling laws are manifesting are the generic, universal, mathematical, topological properties of networks.

The question is, what are the principles that are governing these networks that are independent of design? After a lot of work we postulated the following, just to give an idea.

First, they have to be space filling. They have to go everywhere. They have to feed every cell, every piece of the organism.

Secondly, they have things like invariant units. That is when you evolve from a human being to a whale (to make it a simple story) you do not change the basic units. The cells of the whale or the capillaries of whale, which are the kind of fundamental units, are pretty much indistinguishable from yours and mine. There is this invariance. When you evolve to a new species, you use the same units but you change the network. That's the idea in this picture.

And the last one is of the infinitude of networks that have these properties - space filling and invariant total units. The ones that have actually evolved by the process of continuous feedback implicit in natural selection are those that have in some way optimized the system.

For example, the amount of work that your heart has to do to pump blood around your circulatory system to keep you alive is minimized with respect to the design of the system. You can put it into mathematics. You have a network theory, you mathematize the network, and then you make variations of the network and ask what is the one that minimizes the amount of energy your heart has to use to pump blood through it.

The principle is simple. Mathematically, it is quite complicated and challenging, but you can solve all of that. And you do that so that you can maximize the amount of energy you can put into fitness to make children. You want to minimize the amount of energy just to keep you alive, so that you can make more babies. That's the simplest big picture.

All of those results about scaling are derived. A quarter, four, emerges. And what is the four? It turns out the four isn't a four. The four is actually a "three plus one", meaning it's the dimensionality of the space we live in plus one, which is actually to do, loosely speaking, with the fractal nature of these networks, the fact that there's a sub-similar property.

In D dimensions, you read D plus one (that's my physicist self speaking). Instead of being three quarters for metabolic rate, it would be D over D plus one.

Life in some funny way is actually five dimensional. It's three space, one time, and one kind of fractal. That's five. So we're kind of five dimensional creatures in some curious way, mathematically.

This network theory was used to predict all kinds of things. You can answer questions like why is it we sleep eight hours. Why does a mouse have to sleep 15 hours? And why does an elephant only have to sleep four and a whale two? Well, we can answer that. Why do we evolve at the rate we do? How does cancer work in terms of vasculature and its necrosis? And so on.

A whole bunch of questions can follow from this. One of the most important is growth. Understanding growth. How do we grow? And why do we stop growing, for example? Well, we can answer that. The theory answers that. And it's quite powerful, and it explains why it is we have this so-called sigmoidal growth where you grow quickly and then you stop. And it explains why that is and it predicts when you stop, and it predicts the shape of that curve for an animal.

Here is this wonderful body of work that explains many things — some fundamental, some to do with very practical problems like understanding sleep, aging. The question is, can we take that over to other kinds of network systems. One of the obvious types of systems is a city. Another obvious one is a company. The first question you have to ask is, okay, this was based on the observation of scaling. Scaling was the window. It's interesting of itself, but actually, it's more interesting as a revelatory tool to open onto fundamental principles.

What did we learn from scaling in biology? We not only learned the network theory, but we learned that despite the fact that the whale lives in the ocean, the giraffe has a long neck, and the elephant a truck, and we walk on two feet and the mouse scurries around, at some 85, 90 percent level, we're all scaled versions of one another.

There's kind of one mammal, and every other mammal, no matter what size it is and where it existed, is actually some well-defined mathematically scaled version of that one master mammal, so to speak. And that is kind of amazing.

In other words, the size of a mammal, or any organism for that matter, can tell you how long it should live, how many children it should have, how oxygen diffuses across its lungs, what is the length of the ninth branch of its circulatory system, how its blood is flowing, how quickly it will grow, et cetera.

A provocative question is, is New York just a scaled up San Francisco, which is a scaled up Santa Fe? Superficially, that seems unlikely because they look so different, especially Santa Fe. I live in Santa Fe and it's a bunch of dopey buildings, and here I am in New York overwhelmed by huge skyscrapers.On the other hand, a whale doesn't look much like a giraffe. But in fact, they're scaled versions of one another, at this kind of cross-grained 85, 90 percent level.

Of course, you can't answer this question just by sitting in an armchair. You have to go out and get the data and ask, “If I look at various metrics describing a city, do they scale in some simple way?”

Is there one line, so to speak, upon which all of them sit? Or when I look at all these metrics and I plot them, do I just see this random mess, which says that each city is unique and dominated by its geography and its history? In which case there's not much you can do, and you've got to attack and think about cities as individual.

I got into this work, because first of all, I believe it's a truly challenging, fundamental, science problem.

I think this is very much science of the 21st century, because it is the kind of problem that scientists have ignored. It is under the umbrella of a complex adaptive system and we need to come to terms with understanding the structure and dynamics and organization of such systems because they're the ones that determine our lives and our extraordinary phenomenon that we have developed on this planet.

Can we understand them as scientists? The prevailing way of investigating them is social sciences and economics — which have primarily less to do with generic principles and more to do with case studies and narrative (which is of course, very important). But the question is, can we complement them and make a science of cities, so to speak, and a science of corporations?

It is a very important question, certainly for scaling, because if it's true that every city is unique, then of course, there's no real science of cities. Every case would be special.

Another remarkable fact is that the planet has urbanizing at an exponential rate. Namely, 200 years ago, here sitting in Manhattan, almost everything around me would be a field. There would be a teeny settlement down at Wall Street somewhere of a small number of people. But most of the people would be living in these fields all the way up Manhattan into upstate New York. Indeed, at that time, less than four percent of the United States was urban. Primarily, it was agricultural. And now, only 200 years later, it's almost the reverse. More like 82 percent is urban and less than 20 percent is agricultural. This has happened at an extraordinarily fast rate — and in fact, faster than exponential.

The point to recognize is that all of the tsunami of problems we're facing, from global warming, the environment, to the questions of financial markets and risk, crime, pollution, disease and so forth, all of them are urban.

They all have their origin in cities. They have become dominant since the Industrial Revolution. Most importantly, they've been with us for the last two or 300 years, and somehow, we've only noticed them in the last ten or 15 years as if they'd never been here. Why? Because they've been increasing exponentially. We are on an exponential.

Cities are the cause of the problem, and they're also the cause of the good life. They are the centers of wealth creation, creativity, innovation, and invention. They're the exciting places. They are these magnets that suck people in. And that's what's been happening. And so they are the origin of the problems, but they are the origin of the solutions. And we need to come to terms with that, and we need to understand how cities work in a more scientific framework, meaning to what extent can we make it into a quantitative predictive, mathematizible kind of science.

Is that even possible? And is it useful? That's quest.

The first thing was to ask the question, do they scale? I put together a wonderful team of people, and I'd like to mention their names, because they play an extremely important and seminal role.

One is a man named Luis Bettencourt also a physicist who is at Los Alamos and the Santa Fe Institute. A man named José Lobo, who was at Cornell when I first got him involved, an urban economist and now he's at Arizona State. Another is a student, Deborah Strumsky, who was at Harvard when she joined us, and is now at the University of North Carolina. And there are others, but these were the main characters. Most importantly, they were people that were part of a trans-disciplinary kind of group. And they brought together the data. They did the data mining, the statistics, analysis, et cetera. They have the expertise and the credentials.

The result of all of that was a long, tedious kind of process. To make a long story short, indeed, we found that cities scaled. Just amazing. Cities do scale. Not only do they scale, but also there's universality to their scaling. Let me just tell you a little bit about of what we discovered from the data to begin with.

The first result that we actually got was with my German colleagues, Dirk Helbing, and his then student, Christian Kuhnert, who then worked with me. One of the first results was a very simple one —the number of gas stations as a function of city size in European cities.

What was discovered was that they behaved sort of like biology. You found that they are scaled beautifully, and it scaled as a power law, and the power law was less than one, indicating an economy of scale. Not surprisingly, the bigger the city, the less gas stations you need per capital. There is an economy of scale.

But it's scaled! That is, it was systematic! You tell me the size of a city and I'll tell you how many gas stations it has — that kind of idea. And not only that, it's scaled at exactly the same way across all European cities. Kind of interesting!

But then, we discovered two things later that were quite remarkable. First, every infrastructural quantity you looked at from total length of roadways to the length of electrical lines to the length of gas lines, all the kinds of infrastructural things that are networked throughout a city, scaled in the same way as the number of gas stations. Namely, systematically, as you increase city size, I can tell you, roughly speaking, how many gas stations there are, what is the total length of roads, electrical lines, et cetera, et cetera. And it's the same scaling in Europe, the United States, Japan and so on.

It is quite similar to biology. The exponent, instead of being three quarters was more like .85. So it's a different exponent, but similar. But it's an economy of scale.

The truly remarkable result was when we looked at quantities that I will call “socioeconomic”. That is, quantities that have no analog in biology. These are quantities, phenomena that did not exist until about 10,000 years ago when men and women started talking to one another and working together and forming serious communities leading to what we now call cities, i.e. things like wages, the number of educational institutions, the number of patents produced, et cetera. Things that have no analog in biology, things we invented.

And if you ask, first of all, do they scale? The answer is yes, in a regular way. Then, how do they scale? And this was the surprise to me; I'm embarrassed to say. It should have been obvious prior, but they scaled in what we called a super linear fashion. Instead of being an exponent less than one, indicating economies of scale, the exponent was bigger than one, indicating what economists call increasing returns to scale.

What does that say? That says that systematically, the bigger the city, the more wages you can expect, the more educational institutions in principle, more cultural events, more patents are produced, it's more innovative and so on. Remarkably, all to the same degree. There was a universal exponent which turned out to be approximately 1.15 which translated to English says something like the following: If you double the size of a city from 50,000 to a hundred thousand, a million to two million, five million to ten million, it doesn't matter what, systematically, you get a roughly 15 percent increase in productivity, patents, the number of research institutions, wages and so on, and you get systematically a 15 percent saving in length of roads and general infrastructure.

There are systematic benefits that come from increasing city size, both in terms of the individual getting something — which attracts people to the city, and in terms of the macroscopic economy. So the big cities are good in this sense.

However, some bad and ugly come with it. And the bad and ugly are things like a systematic increase in crime and various diseases, like AIDS, flu and so on. Interestingly enough, it scales all to the same 15 percent, if you double the size. Or put slightly differently, another way of saying it is, if you have a city of a million people and you broke it down into ten cities of a hundred thousand, you would require for that ten cities of a hundred thousand, 30 to 40 percent more roads, and 30 to 40 percent general infrastructure. And you would get a systematic decrease in wages and productivity and invention. Amazing. But you'd also get a decrease in crime, pollution and disease, systematically. So there are these trade-offs.

What does this mean? What is this coming from? And what do they imply? Let me just say one of the things that they imply.

If cities are dominated by wealth creation and innovation, i.e. the super linear scaling laws, there's increasing returns to scale. How does that impact growth? What does that do for growth? Well, it turns out, of course, had it been biology and it had been dominated by economies of scale, you would have got a sigmoid curve, and you would have stopped growing. Bad for cities, we believe, and bad for economies.

Economies must be, in a capitalist system, ever expanding. It's good that we have super linear scaling, because what that says is you have open-ended growth. And that's very good. Indeed, if you can check it against data, it agrees very well. But there's something very bad about open-ended growth.

One of the bad things about open-ended growth, growing faster than exponentially, is that open-ended growth eventually leads to collapse. It leads to collapse mathematically because of something called finite times singularity. You hit something that's called a singularity, which is a technical term, and it turns out as you approach this singularity, the system, if it reaches it, will collapse. You have to avoid that singularity in order to stop collapsing. It's great on the one hand that you have this open ended growth. But if you kept going, of course, it doesn't make any sense. Eventually, you run out of resources anyway, but you would collapse. And that's what the theory says.

How do you avoid that? Well, how have we avoided it? We've avoided it by innovation. By making a major innovation that so to speak, resets the clock and you can kind of start over again with new boundary conditions. We've done that by making major discoveries or inventions, like we discover iron, we discover coal. Or we invent computers, or we invent IT. But it has to be something that really changes the cultural and economic paradigm. It kind of resets the clock and we start over again.

There's a theorem you can prove that says that if you demand continuous open growth, you have to have continuous cycles of innovation. Well, that's what people believe, and it's the way people have suggested that’s how you get out of the Malthusian paradox. This all agrees within itself but there is a huge catch.

I said earlier that in biology you have economies of scale, scaling that is sub linear, three quarters less than one, and that the pace of life gets slower the bigger you are. In cities and social systems, you have the opposite. You have the super linear scaling. You have increasing returns to scale. The bigger you are, the more you have rather than less.

It turns out when you go through the theoretical framework that leads to the opposite to biology the pace of life increases with size. So everything that's going on in New York today is systematically going faster than it is in San Francisco, than it is in Santa Fe, even the speed of walking.

There's data, and if you plot it, you will see that the speed of walking in cities, actually, I said the data is actually taken primarily in European cities, but you can see this systematic increase in some reasonable agreement with the theory.

The first thing is that we have this increasing pace of life. We have open-ended growth, increase in pace of life, and the threat of collapse because of the singularity. But there's a big catch about this innovation. Theory says, sure, you can get out of collapse by innovating, but you have to innovate faster and faster.

Something that took 10,000 years 20,000 years ago to make a change, now takes 25 years. So this is not the clock that is governing social life. There's a clock that's getting faster and faster. And so you have to innovate faster and faster in order to avoid the collapse. And it all comes out of this exponential growth driven by super linear scaling.

The question then is, is this sustainable? The system will collapse, because eventually you would have to be making a major innovation, like you know, IT every six months. Well, that's completely crazy. First of all, we're human beings. We can't adapt to that, even. But we can't do it, so this is very threatening.

This leads then to all kinds of questions about global sustainability and how can you construct a conceptual framework that gives rise to having wealth creation, innovation, this kind of quality and standard of life, wealth production, and yet, not grow in such a way that you are probing the singularity and collapsing. That's the challenge. That's certainly something that we have to face.

Let me just say a few words about ideas as to why it is there's scaling in cities. What we've shown is that there's universality that on the one hand, you have this sub linear scaling, economies of scale for infrastructure like biology. But the dominant part of the city, wealth creation, innovation and the socio economic kinds of quantities, that have no analog in biology, scale super linearly.

This is true for any metric you want to think of and across the world. If you look at Japanese data or Chinese data or data from Chile or Colombia or the Netherlands or Portugal or the United States, it all looks the same. Yet these cities have nothing to do with one another.

It says that geography and history played a subdominant role as it did in biology in a sense. And so if you tell me the size of a city in the United States, I can tell you with some 85 percent accuracy how many police it would have, how many AIDS cases, how long the length of the roads are, how many patents it's producing and so on, on the average.

Of course, you can use that as a baseline for talking about actual individual cities, how they over and underperform relative to this idealized scaling number. But the question is, where in the hell does that come from? What is it that's universal that transcends countries and cultures?

Well obviously, it's what cities are really about, not these buildings and the roads and things, but the people. It's people. What we believe is that the scaling laws are a manifestation of social networks, of the universality of the way human beings interact, what we're doing now, talking to one another, exchanging ideas, and doing tasks together, and so on.

It is the nature of those networks and the clustering — very importantly, the hierarchical clustering of those networks, the family structure, the way families interact, and then all the way out through businesses and so on, that there's a kind of universality to that that is representative of the kind of scale at which humans interact.

For example, even though families in China and the United States traditionally may look different, most people cannot interact seriously, in a serious, dedicated way with more than five or six people. It doesn't matter how big the family is actually. Despite Facebook, you cannot have a hundred best friends anywhere in the world.

These things are representative of the universal nature of the social networking. Our belief is that it is the nature of that and the hierarchy of it. For example, not only the hierarchy in size, but the hierarchy in the fact that you're strongest interaction is with your family. You have a much weaker interaction with your colleagues in your job, and in your job situation, you have a much weaker interaction even with the CEO of the company, and all the way around the hierarchy. There is this presumed self-similar structure that goes up through the hierarchy in terms of the size of the hierarchy and in terms of the strength of interaction.

We believe it is that hierarchy which is transcending all of the aspects of the city and is being represented by these kinds of laws. So how is it that when we plot, we can plot GDP of the city, the number of AIDS cases and wages on one plot, and they overlap one another? They're just the same line. Well, that's because from this viewpoint, they're all manifestations of people interacting with one another.

The last piece of this is to take it to companies. Again, I must say that when I first started working on this, I just assumed companies were little cities so to speak. I also assumed they were dominated by creativity and so on.

It took us a long time to get data for companies, because unlike cities, you have to pay for that data. But we've just done it.

This is very much a work in progress and incipient, and some of this will have to be amended, but the results of all of the preliminary analyses as yet unpublished are that companies scale.

In fact, we've done it primarily without paying attention to sector, although we've done some decomposition into sector. What I'm going to talk about here is regardless of sector. If you just take all companies equally for a moment, indeed, what you see if you plot the various metrics of a company from sales and profits, taxation, assets versus company size, using the metric of employees (you could use others — you could use sales itself but we used employees) you find scaling.

There's much more variation, many more outliers among companies than there are among cities, and more among cities than there are among organisms. But nevertheless, you see very good evidence of scaling. And the thing that surprised us about this scaling was that it was like biology, not like cities. It was sub linear predominately.

That was surprising because sub linear in the kind of conceptual framework we developed was a reflection of economies of scale, and super linear as a reflection of wealth creation and innovation. It is said that predominately companies are dominated by economies of scale rather than innovation.

If it were dominated by economies of scale, sub linear scaling, unlike cities (which have open ended growth) companies would grow and then stop growing. And not only that, if you extrapolated from biology, they would indeed, die, ultimately.

We looked at the growth curves as the metrics of the company, like its assets or its profits, as a function of time, or its number of employees as a function of time. Indeed, the generic behavior is a sigmoid. They grow fast and they stop. All the big companies stop at roughly the same value, which is intriguing of it self. I think that number is about half a trillion dollars.

We have a wonderful graph that has about ten thousand companies plotted on one graph and they are these growth curves. You see this kind of spaghetti looking graph by just eyeballing it. Everything grows and stops growing. That's what it looks like. We're still in the middle of analyzing a lot of this.

The picture emerges. Companies are more like organisms. They grow and asymptote. Cities are open ended.

More importantly, what we discovered is that on the one hand, sales increased linearly with company size. On the other hand, profits increased sub linearly of an exponent of about one eighth. This data is all U.S. data on publicly traded companies.

Sales to profits are systematically decreasing so that eventually, the profit to sales margin is going to zero. If you just extrapolate this, indeed, if you look at the data, you see that the fluctuations in all these quantities are proportional to the size of the company. The fluctuation is getting bigger and bigger. The profits are decreasing relative to sales. Even though the profits are increasing the bigger you are, where you think, "we made several billion dollars" what you realize is that you're in an environment where the fluctuation is eventually bigger than that. This is possibly the mechanism by which companies die.

Let me tell you the interpretation. Again, this is still speculative.

The great thing about cities, the thing that is amazing about cities is that as they grow, so to speak, their dimensionality increases. That is, the space of opportunity, the space of functions, the space of jobs just continually increases. And the data shows that. If you look at job categories, it continually increases. I'll use the word "dimensionality." It opens up. And in fact, one of the great things about cities is that it supports crazy people. You walk down Fifth Avenue, you see crazy people, and there are always crazy people. Well, that's good. It is tolerant of extraordinary diversity.

This is in complete contrast to companies, with the exception of companies maybe at the beginning (think of the image of the Google boys in the back garage, with ideas of the search engine no doubt promoting all kinds of crazy ideas and having maybe even crazy people around them).

Well, Google is a bit of an exception because it still tolerates some of that. But most companies start out probably with some of that buzz. But the data indicates that at about 50 employees to a hundred, that buzz starts to stop. And a company that was more multi dimensional, more evolved becomes one-dimensional. It closes down.

Indeed, if you go to General Motors or you go to American Airlines or you go to Goldman Sachs, you don't see crazy people. Crazy people are fired. Well, to speak of crazy people is taking the extreme. But maverick people are often fired.

It's not surprising to learn that when manufacturing companies are on a down turn, they decrease research and development, and in fact in some cases, do actually get rid of it, thinking "oh, we can get that back, in two years we'll be back on track."

Well, this kind of thinking kills them. This is part of the killing, and this is part of the change from super linear to sublinear, namely companies allow themselves to be dominated by bureaucracy and administration over creativity and innovation, and unfortunately, it's necessary. You cannot run a company without administrative. Someone has got to take care of the taxes and the bills and the cleaning the floors and the maintenance of the building and all the rest of that stuff. You need it. And the question is, “can you do it without it dominating the company?” The data suggests that you can't.

The question is, as a scientist, can we take these ideas and do what we did in biology, at least based on networks and other ideas, and put this into a quantitative, mathematizable, predictive theory, so that we can understand the birth and death of companies, how that stimulates the economy? How it's related to cities? How does it affect global sustainability and have a predictive framework for an idealized system, so that we can understand how to deal with it and avoid it? If you're running a bigger company, you can recognize what the metrics are that are driving you to mortality, and possibly put it off, and hopefully even avoid it.

Otherwise we have a theory that tells you when Google and Microsoft will eventually die, and die might mean a merger with someone else.

"This remarkable collection of fluent and fascinating essays reminds me that there is almost nothing as spine-tinglingly exciting as glimpsing a new nugget of knowledge for the first time. These young scientists give us a treasure trove of precious new insights." — Matt Ridley[6], Author, The Rational Optimist

"I would have killed for books like this when I was a student!" — Brian Eno[7], Composer; Recording Artist; Producer: U2, Cold Play, Talking Heads, Paul Simon

"Future Science shares with the world a delightful secret that we academics have been keeping — that despite all the hysteria about how electronic media are dumbing down the next generation, a tidal wave of talent has been flooding into science, making their elders feel like the dumb ones..... It has a wealth of new and exciting ideas, and will help shake up our notions regarding the age, sex, color, and topic clichés of the current public perception of science." — Steven Pinker[8], Johnstone Family Professor, Department of Psychology, Harvard; Author, The Language Instinct

I knew of Geoffrey West thirty years ago or more when we both worked on the parton model in theoretical particle physics. I just read the Edge interview this evening. It's a beautiful description of the application of the techniques of physics to the social sciences in a way that recognizes and respects the essential nature of the objects it focuses on. When physical scientists tackles the social sciences they often seek laws like the laws of physics, and their models end up simplifying the object. This doesn't -- it seems to combine observation and theorizing in such productive proportions. The Edge description of West's work is inspiring. I spent a summer at Santa Fe a few years ago working on my book, and I wish I had spent more time learning then what Geoffrey had been doing.

It was delightful to listen to Geoffrey West explain how he and his team are expanding their work on cities into the realm of corporations. West divulges that the data from the 10,000 or so publicly traded corporations in the U.S. suggest that, as they grow, companies become less innovative and more "uni-dimensional". I wonder whether West et al. have already made or intend to make comparisons to privately held companies. Could the number of employees actually be a a close approximation for a company's transition from being privately controlled to publicly traded? Perhaps privately held companies continue to innovate, even as they increase in size? I really look forward to following this work and finding out whether, when it comes to commerce, small is still beautiful.